spCAMPAIGNS_SendEmail is the right place to start.  This procedure adds a record to EMAILMAN for each email to be sent. If nothing is getting inserted, then you will want to look at vwCAMPAIGNS_Send.  This view does some complicated joins to determine the emails that need to be sent. 

You are going to have to start at the top of the table joins to discover the problem.  First, get a valid Campaign ID.  I'm going to abbreviate the campaign ID as 98765.

1. Check to make sure that there are email marketing records asssociated with the campaign.
   select * from EMAIL_MARKETING where CAMPAIGN_ID = 98765

2. Check to make sure that there are prospects associated with the campaign.
   select * from PROSPECT_LIST_CAMPAIGNS where CAMPAIGN_ID = 98765

3. Check to make sure that there are valid email associated with the prospect lists.
   select * from PROSPECT_LIST_CAMPAIGNS 
  inner join vwPROSPECT_LISTS_Emails
  on vwPROSPECT_LISTS_Emails.ID = PROSPECT_LIST_CAMPAIGNS.PROSPECT_LIST_ID
  where CAMPAIGN_ID = 98765

There are two more joins, but it would be useful to know if we have results.  If we have no results at this stage, then the place to look is the vwPROSPECT_LISTS_Emails view.